### Conjugation spaces.

Hausmann, Jean-Claude, Holm, Tara, Puppe, Volker (2005)

Algebraic & Geometric Topology

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Hausmann, Jean-Claude, Holm, Tara, Puppe, Volker (2005)

Algebraic & Geometric Topology

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Tamanoi, Hirotaka (2003)

Algebraic & Geometric Topology

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Elezi, Artur (2003)

International Journal of Mathematics and Mathematical Sciences

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Živaljević, Rade T. (1998)

Publications de l'Institut Mathématique. Nouvelle Série

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Ugo Bruzzo, Vladimir Rubtsov (2012)

Open Mathematics

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We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.

Indranil Biswas, S. Senthamarai Kannan, D. S. Nagaraj (2015)

Complex Manifolds

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Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection. We show some relationship between the condition that EH admits a G–equivariant structure and the condition that EH admits a (flat) G–connection. The cases of bundles on homogeneous spaces and smooth toric varieties are discussed.

Graeme Segal (1968)

Publications Mathématiques de l'IHÉS

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Teleman, Constantin (2000)

Annals of Mathematics. Second Series

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Dieter Erle (1975)

Compositio Mathematica

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Gross, Christian

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The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps $U:M\to {\text{SU}}_{{N}_{F}}$ he thinks of the meson fields as of global sections in a bundle $B(M,{\text{SU}}_{{N}_{F}},G)=P(M,G){\times}_{G}{\text{SU}}_{{N}_{F}}$. For calculations within the skyrmion bundle the author introduces by means of the so-called equivariant cohomology an analogue of the topological charge and the Wess-Zumino term. The final result of this paper is the following Theorem. For the skyrmion bundle with ${N}_{F}\le 6$, one has $${H}^{*}\left(EG{\times}_{G}{\text{SU}}_{{N}_{F}}\right)\cong {H}^{*}{\left({\text{SU}}_{{N}_{F}}\right)}^{G}\cong \text{S}\left({\underline{G}}^{*}\right)\otimes {H}^{*}\left({\text{SU}}_{{N}_{F}}\right)\cong {H}^{*}\left(BG\right)\otimes {H}^{*}\left({\text{SU}}_{{N}_{F}}\right),$$ where $EG(BG,G)$ is the universal...